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Prediction of natural frequencies of Rayleigh pipe by hybrid meta-heuristic artificial neural network

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Abstract

This paper focuses on determination of the natural frequencies in slenderness pipe flows by considering fluid–structure interaction approach. Rayleigh beam theory is used to model the pipe. The fluid in the pipe is assumed as ideal, steady and uniform. Hamilton’s variation principle is demonstrated to obtain the equation of motion of pipe–fluid system. The dimensionless partial differential equations of motion are converted into matrix equations, and the values of natural frequencies of first three modes are archived with the analytical method. The results are arranged to be a data set for hybrid meta-heuristic artificial neural network (ANN) method. Three different meta-heuristic algorithms are used to train the ANN: particle swarm optimization (PSO) and artificial bee colony (ABC) and grey wolf optimizer (GWO). The comparison is presented to find a suitable algorithm based on accuracy for determining the natural frequency of the Rayleigh pipe conveying fluid. The results show that the PSO algorithm outperforms the other meta-heuristics in terms of performance indicators in prediction analysis. However, all algorithms and models can predict the natural frequencies with rate with satisfactory accuracy.

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Abbreviations

a y :

Acceleration

A p :

Cross-sectional areas of the pipe

A f :

Cross-sectional areas of the fluid

E :

Young’s modulus of the pipe material

J p :

Moment of inertia of the pipe

L :

Straight and uniform length of pipe

P :

Pressure

T :

Total kinetic energy

t* :

Time

u :

Axial fluid velocity

U :

Elastic potential energy

x* :

Spatial coordinate

w*:

Transverse displacement

Ρ p :

Density of the pipe

Ρ f :

Density of the fluid

y* :

Vertical displacement of the pipe

Y:

Vertical force

\(\vec{A}\), \(\vec{C}\) :

Coefficient vectors

D :

The number of parameters to be optimized

d r (L) (t) :

The r-th expected vector of the t-th teaching sample

εr (L) :

Prediction nonlinear error

F(θ i ) :

The nectar amount of the food source

m p :

Mass of the pipe

m f :

Mass of the fluid

Q :

Samples’ number

θ i :

Position of the food source

p i :

Probability value

R :

Standard deviation coefficient

s :

Number of food source

λ :

Slenderness ratio

ω :

Natural frequencies

β :

Mass ratio

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Authors and Affiliations

  1. Vocational School of Manisa Technical Sciences, Manisa Celal Bayar University, Manisa, Turkey

    Begum Yurdanur Dagli

  2. Faculty of Engineering, Civil Engineering Department, Manisa Celal Bayar University, Manisa, Turkey

    Abdulkerim Ergut & Mustafa Erkan Turan

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  1. Begum Yurdanur Dagli
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  2. Abdulkerim Ergut
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Correspondence to Begum Yurdanur Dagli.

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Dagli, B.Y., Ergut, A. & Turan, M.E. Prediction of natural frequencies of Rayleigh pipe by hybrid meta-heuristic artificial neural network. J Braz. Soc. Mech. Sci. Eng. 45, 221 (2023). https://doi.org/10.1007/s40430-023-04156-3

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